薄板弯曲和振动分析的区间B样条小波有限法

基于二维张量积区间B样条小波及小波有限元理论,研究了用于薄板静动力学分析的区间B样条小波有限元法。在小波有限元用于薄板分析的列式过程中,采用区间B样条小波尺度函数对横向位移场逼近,从矩形和斜形薄板静动力学势能泛函出发,由变分原理得到小波有限元求解方程。该方法具有B样条函数数值逼近精度高和多种用于结构分析的小波基函数的特点。数值算例表明:区间B样条小波有限元法能以很少的计算自由度获得与其它方法同样的计算精度。

FINITE ELEMENT METHOD OF B-SPLINE WAVELET ON THE INTERVAL FOR THIN PLATE BENDING AND VIBRATION ANALYSIS

Based on two-dimensional tensor product B-spline wavelet on the interval (BSWI) and wavelet finite element method (WFEM), a finite element method (FEM) of BSWI is investigated to solve the static and vibration problems of thin plates. In the progress of WFEM formulation for thin plate analysis, BSWI scaling functions are employed to approximate the transverse displacements field. From the generalized function of potential energy for rectangle and skew plates, we can obtain the solving equation of WFEM via variational principle. The method combined the versatility of the accuracy of B-spline function approximation and various basis functions for structural analysis. Some numerical examples are studied to verify the proposed method. With few computational degree of freedoms (DOFs), the numerical results of the presented method are in good agreement with the solutions of other methods.